Amy Greenwald is Professor of Computer Science at Brown University in Providence, Rhode Island. Her core research focus is multiagent AI. Application areas include supply chains, electricity markets, and online advertising. She frames such environments as games or economies, and develops algorithms to solve for their equilibria and/or builds strategic AI for these environments. Greenwald did postdoctoral work at IBM Research and was a visiting researcher at Microsoft Research. She was awarded the Presidential Early Career Award for Scientists and Engineers (PECASE), a Fulbright (which she declined), and a Sloan Fellowship. Finally, Greenwald is active in promoting diversity in Computer Science, leading multiple K-12 initiatives in which Brown undergraduates teach computer science to public school students in the greater Providence area.

Integer bilevel programming problems are known to be very challenging due to the lack of strong relaxations that can be efficiently computed. We propose single-level representations of integer bilevel programming problems that rely on network flow-based approximations of the follower's value function, using decision diagrams. We then show how we can derive scalable relaxations from this representation by constructing a minorizer of the follower’s value function. We experimentally compare our approach with state-of-the-art bilevel programming solvers and show that we can obtain competitive results for certain problem classes.

Leonardo Lozano is an associate professor in the Operations, Business Analytics & Information Systems Department at the University of Cincinnati. He received his B.Sc. degree from Universidad de los Andes, his M.Sc. degree from University of Florida, and his Ph.D. degree from Clemson University. His research focuses on exact algorithms for discrete optimization and has been published in Operations Research, Mathematical Programming, Transportation Science, Networks (Glover-Klingman 2020 best paper award), and INFORMS Journal on Computing, among others. His research has been funded by the Office of Naval Research, the Air Force Office of Scientific Research, and Google.

Bilevel optimization has emerged as a central paradigm in modern optimization, driven by a wide range of applications in machine learning, data science, and engineering. Over the past decade, the field has witnessed significant advances in both algorithmic development and theoretical understanding, particularly for convex bilevel optimization problems. In this talk, we will review recent progress in the design and analysis of algorithms for bilevel optimization, including convergence guarantees and complexity results. We will discuss key challenges that distinguish bilevel problems from classical optimization models, highlight representative contributions, and outline several important open questions.

Dr. Shoham Sabach is an Associate Professor in the School of Operations Research and Information Engineering at Cornell University. Since 2022, he has held an appointment as an Amazon Scholar at Amazon Research. He received his Ph.D. in Mathematics from the Technion – Israel Institute of Technology in 2012. His research focuses on the theory, algorithms, and applications of optimization, with particular emphasis on developing computationally efficient methods and bridging optimization with problems arising in science, engineering, and AI. Dr. Sabach serves on the editorial boards of several leading optimization journals, including Mathematics of Operations Research and Mathematical Programming. He was awarded the 2017 SIAM Optimization Prize for the best optimization paper published between 2014 and 2017.

Bilevel optimization is a fundamentally important branch of modern mathematical optimization with numerous applications in machine learning, artificial intelligence, data science, operations research, and engineering. In this lecture, we will present recent advances in first-order methods for continuous bilevel optimization.

We will begin by discussing several important applications of continuous bilevel optimization, particularly in emerging areas such as machine learning. We will then present scalable first-order methods based on hyperobjective and joint-objective formulations for solving several important classes of continuous bilevel optimization problems, along with their first-order oracle complexity guarantees for computing appropriate approximate solutions. Finally, we will present preliminary numerical results to demonstrate the effectiveness of the proposed methods.

Zhaosong Lu is a Full Professor in the Department of Industrial and Systems Engineering at the University of Minnesota. He received his Ph.D. in Operations Research from Georgia Institute of Technology. His research focuses on the theory and algorithms of continuous optimization, with applications in data science and machine learning. Dr. Lu has published extensively in leading journals such as Mathematical Programming, Mathematics of Operations Research, and SIAM Journal on Optimization. His work has been supported by funding agencies including AFOSR, NSF, and ONR. He has served on several prize committees, such as the INFORMS George Nicholson Prize and the ICCOPT Best Paper Award. In addition, he has served as an Associate Editor for journals including Mathematics of Operations Research, SIAM Journal on Optimization, Computational Optimization and Applications, and Journal of Global Optimization.

We discuss selected topics in mixed-integer bilevel optimization, focusing on features that distinguish this class of problems from single-level linear and mixed-integer linear optimization problems. We begin with motivating application examples that naturally lead to bilevel models with integrality restrictions on some or all decision variables. We then review classical and recent theoretical results on the computational complexity of bilevel optimization problems. Finally, we outline the main ideas behind exact and heuristic solution methods, with particular emphasis on recent developments.

Dr. Oleg A. Prokopyev is a Professor of Quantitative Business Administration at the University of Zurich (UZH), Switzerland. Previously, he was a professor in the Department of Industrial Engineering at the University of Pittsburgh. He earned his M.S. and B.S. in Applied Mathematics and Physics from the Moscow Institute of Physics and Technology, and he received his Ph.D. in Industrial and Systems Engineering from the University of Florida. Dr. Prokopyev has published more than 100 journal papers. One of his co-authored papers received the William Pierskalla Best Paper Award by the Health Applications Society of the Institute for Operations Research and the Management Sciences (INFORMS), while another received the Best Publication Award in Environment and Sustainability by the INFORMS Section on Energy, Natural Resources, and the Environment. He was also the recipient of the Air Force Office of Scientific Research (AFOSR) Young Investigator Research Program (YIP) Award. His research interests lie at the intersection of mathematical optimization theory and the development of computational and algorithmic methods. Dr. Prokopyev serves as a Co-Editor-in-Chief of Optimization Letters and as editorial board member of several other journals.